Understanding Hyperbolas

This video tutorial covers the conversion of hyperbola equations from general to standard form and demonstrates how to graph hyperbolas. It reviews key concepts such as the transverse axis, center, and asymptotes, and provides step-by-step examples for graphing hyperbolas with both horizontal and vertical axes.

What is the primary goal of this video on hyperbolas?

• To solve quadratic equations

• To convert and graph hyperbolas

• To understand parabolas

• To learn about ellipses

In the standard form of a hyperbola, what does the positive part of the equation determine?

• The center of the hyperbola

• The position of the foci

• The direction of the transverse axis

• The length of the asymptotes

How do you determine the value of C in a hyperbola's equation?

• C = A - B

• C squared = A squared - B squared

• C = A + B

• C squared = A squared + B squared

What is the purpose of constructing a rectangle when graphing a hyperbola?

• To find the center

• To determine the foci

• To calculate the area

• To sketch the asymptotes

When graphing a hyperbola with a horizontal transverse axis, how are the vertices determined?

• By adding and subtracting A from the y-coordinate

• By adding and subtracting B from the y-coordinate

• By adding and subtracting A from the x-coordinate

• By adding and subtracting C from the x-coordinate

In the example provided, what is the center of the hyperbola after converting the equation to standard form?

• (2, -1)

• (1, 1)

• (0, 0)

• (-1, 2)

What is the value of A in the first example after converting the equation to standard form?

• 1

• 3

• 4

• 2

In the second example, what is the first step in completing the square?

• Adding 11 to both sides

• Dividing by 4

• Multiplying by 4

• Subtracting 11 from both sides

What is the approximate value of C in the second example?

• 1.41

• 4.47

• 3.16

• 2.24

In the second example, what is the orientation of the transverse axis?

• Horizontal

• Vertical

• Diagonal

• None